What is 10/35 plus 7/21? (Answer: 13/21)

Exact Answer

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Problem: What is 10/35 plus 7/21?
Formula / Expression: 10/35 + 7/21
Final Answer: 13/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 10/35 by 3, and multiply the numerator and denominator of 7/21 by 5 so both fractions share the common base 105.
Working: 10 × 3/35 × 3 = 30/105 and 7 × 5/21 × 5 = 35/105

Step 3: Add the Numerators
Now add the numerators (30 + 35 = 65) and keep the common denominator 105 unchanged.
Working: 30 + 35/105 = 65/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 65 and 105, which is 5. Divide both the numerator and denominator by 5.
Working: 65 ÷ 5/105 ÷ 5 = 13/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).
Working: 13 ÷ 21 = 0.619048 (61.9048%)

Key Values:
- Simplified Fraction: 13/21
- Mixed Number Form: 13/21
- Decimal Value: 0.619048
- Percentage: 61.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-35-plus-7-21/
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10/35 + 7/21 = 13/21

Simplified Fraction

13/21

Mixed Number

Proper (13/21)

Decimal Value

0.619048

Percentage

61.9048%

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Step-by-Step Solution: 10/35 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 10/35 by 3, and multiply the numerator and denominator of 7/21 by 5 so both fractions share the common base 105.

10 × 3/35 × 3 = 30/105 and 7 × 5/21 × 5 = 35/105

Step 3

Add the Numerators

Now add the numerators (30 + 35 = 65) and keep the common denominator 105 unchanged.

30 + 35/105 = 65/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 65 and 105, which is 5. Divide both the numerator and denominator by 5.

65 ÷ 5/105 ÷ 5 = 13/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 21 produces a repeating decimal (approximately 0.619048, or 61.9048%).

13 ÷ 21 = 0.619048 (61.9048%)

Visual Representation

The diagram below illustrates 10/35 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/21`
Mixed Number Form	`13/21`
Decimal Form	`0.619048`
Percentage	`61.9048%`

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Frequently Asked Questions

What is 10/35 plus 7/21 as a fraction?

10/35 + 7/21 in simplest fraction form is 13/21.

What is 10/35 plus 7/21 as a decimal?

10/35 + 7/21 converted to a decimal is 0.619048.

What is 10/35 plus 7/21 as a percentage?

10/35 + 7/21 expressed as a percentage is 61.9048%.

Does 10/35 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.619048...) because the denominator contains prime factors other than 2 and 5.